Module Title:   Statistics (Discrete and Continuous)

Module Credit:   20

Module Code:   CM-0123L

Academic Year:   2015/6

Teaching Period:   Semester 1

Module Occurrence:   A

Module Level:   FHEQ Level 4

Module Type:   Linked 10+10

Provider:   Computer Science

Related Department/Subject Area:   School of Computing, Informatics and Media (Mathematics)

Principal Co-ordinator:   Dr A Csenki

Additional Tutor(s):   -

Prerequisite(s):   None

Corequisite(s):   None

Aims:
To present an introduction to the principle of randomness through event theory, random samples and discrete variables. To extend the concepts to continuous random variables, estimation and sampling, and elementary statistical inference.

Learning Teaching & Assessment Strategy:
The basic theory and illustrative examples are presented and developed in formal lectures. Complementary tailor-made example sheets are provided. These are discussed, and assistance with their solution is provided in tutorials, either on a one-to-one basis or as a staff or student-led group, as appropriate.

Formative assessment assignments encourage the ongoing digestion of the material, with the extent of the cumulative knowledge and skills acquired assessed through two coursework assignments and a formal examination.

Lectures:   36.00          Directed Study:   137.50           
Seminars/Tutorials:   24.00          Other:   0.00           
Laboratory/Practical:   0.00          Formal Exams:   2.50          Total:   200.00

On successful completion of this module you will be able to...

show an understanding of the fundamentals of event theory, random samples and discrete variables, and the basic principles involved in using continuous random variables.

On successful completion of this module you will be able to...

manipulate using the basic principles of event theory and discrete random variables, and apply the underlying properties of mathematical expectation, sample analysis, regression modelling, estimation, sampling and statistical inference.

On successful completion of this module you will be able to...

learn and work independently with patience and persistence using good general skills of organization and time-management, write coherently and clearly communicate results.

  Coursework   25%
 
  2 assignments consisting of questions taking approximately 2 hours to answer per assignment
  Examination - closed book 2.50 75%
 
  Examination
  Examination - closed book 3.00 100%
 
  Supplementary examination

Outline Syllabus:
EVENT THEORY: random; simple and compound events; probability axioms; equally likely; combinatorics; conditional; multiplication; total probability; Bayes` theorem; stochastic independence. DISCRETE RANDOM VARIABLES: binomial family; geometric; discrete uniform; Poisson approximation to binomial. EXPECTATION (discrete): linear operator; variance; standard deviation; linear functions of X; moments; standard discrete families applications; probability generating function. SAMPLE STATISTICS: mean, variance; location, dispersion measures; transformed and grouped data; graphical methods. REGRESSION MODELS: line fitting observation pairs; least-squares; correlation coefficients, linear regression.

CONTINUOUS RANDOM VARIABLES: p.d.f.; expectation; moments (central, non-central); m.g.f.; exponential and uniform distributions applications; gamma integral; gamma distribution; Weibull distribution. GAUSSIAN NORMAL FAMILY: standard tables; standardization; variables transformation; normal m.g.f.; normal approximation to binomial and Poisson distributions. BIVARIATE DISTRIBUTIONS (discrete): expectation of H(X,Y); covariance; independent random variables; m.g.f. independent random variables sums. ESTIMATION: point; maximum likelihood; moments method; unbiased; consistency; population variance unbiased estimator; confidence intervals; normal population mean.

Version No:  2